Zhu's algebra, the C_2 algebra, and twisted modules

Details Zhu's algebra, the C_2 algebra, and twisted modules Zhu's algebra, the C_2 algebra, and twisted modules

2008-11-24

arxiv.org/abs/0811.3892v1

Mathematics

Quantum Algebra

14 pages

Scientific paper

In his landmark paper, Zhu associated two associative algebras to a vertex operator algebra: what are now called Zhu's algebra and the C_2-algebra. The former has a nice interpretation in terms of the representation theory of the VOA, while the latter only serves as a finiteness condition. In this paper we undertake first steps to unravel the interpretation of the C_2 vector space. In particular we suggest that it seems and controls the twisted representations of the VOA.

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